MHD waves, which are prevalent in the solar and space plasmas, play a key role in energy transport between different locations and consequent energy conversion between waves and particles. In this talk, I will briefly review the observational progress history of the MHD waves in the solar atmosphere, and introduce the physics significance of the MHD waves in shaping the solar dynamics from the perspective of numerical modeling. To be specific, how do we identify the Alfven waves, slow-mode, and fast-mode waves based on the advancement in spectroscopic and imaging observations? How are MHD waves coupled with the background inhomogeneous plasmas with a transition from neutral to ionized state and from collisional to collisionless state? Some challenges to be faced for the topic of MHD waves in the solar atmosphere will also be discussed.